Shift of the Bragg position in grazing-incidence diffraction

Abstract

The intensity distribution in grazing-incidence diffraction along the grazing exit angle, a f, has been generally studied assuming the fulfilment of the Bragg condition, both experimentally and theoretically. We consider deviations of the incidence angle and detector position (θ) from the exact Bragg angle, θ B, as well as variation of the incidence angle with respect to the surface, α i, and lattice mismatching of layered structures. The so-called surface peak is caused by refraction and appears at the fixed angular position of the critical angle of the total external reflection, α c. Beside it an additional peak occurs, that is explained by fulfilling the Bragg condition of the lateral wave vector components of incident and diffracted beams. This corresponds to the intersection of the truncation rod and the Ewald sphere. Therefore its angular position in the diffracted scattering fan depends on both αi and θ − θ B. This additional peak is only visible if α i is below α C or θ > θ B. These considerations have been verified experimentally on an InP layer.